Submission Deadline: You will receive a mark only for the codes that are demonstrated in front of a TA by the end of the lab. Additionally, you have to submit on Avenue a text le (with extension txt) containing each java class that you write (just change the extension java to txt). The name of the le should indicate the name of the class and your student ID number. The online submission has to be done by the end of the lab session.


Description: Write two Java classes: Matrix, which represents matrices with integer ele-ments, and UpperTriangularMatrix to represent upper triangular matrices with integer elements stored e ciently. The accompanying le Matrix.java contains an incomplete declaration of the Matrix class. You need to complete the declarations of incomplete methods or constructors according to the speci cations given below. Additionally, you need to write the declaration of the class UpperTriangularMatrix. A class to test class Matrix and class UpperTriangularMatrix are provided as samples. However, you may need to perform additional testing to ensure that your code meets all the speci cations. A demo class will be provided for the demonstration in the lab.


Specifications: Class Matrix has only the following instance elds, which have to be private:


– an integer to store the number of rows


– an integer to store the number of columns.


– a two dimensional array of integers to store the matrix elements. Class Matrix contains at least the following constructors:


– public Matrix(int row, int col) – constructs a row-by-col matrix with


all elements equal to 0; if row 0, the number of rows of the matrix is set to 3; likewise, if col 0 the number of columns of the matrix is set to 3.


– public Matrix(int[][] table) – constructs a matrix out of the two dimen-sional array table, with the same number of rows, columns, and the same element in each position as array table.


Class Matrix contains at least the following methods:


1) public int getElement(int i, int j) throws IndexOutOfBoundsException – returns the element on row i and column j of this matrix; it throws an ex-ception if any of indexes i and j is not in the required range (rows and columns indexing starts with 0); the detail message of the exception should read: "In-valid indexes".


2) public boolean setElement(int x, int i, int j) – if i and j are valid indexes of this matrix, then the element on row i and column j of this matrix is assigned the value x and true is returned; otherwise false is returned and no change in the matrix is performed.









3) public Matrix copy() – returns a deep copy of this Matrix. Note: A deep copy does not share any piece of memory with the original. Thus, any change performed on the copy will not a ect the original.


4) public void addTo(Matrix m) throws ArithmeticException – adds Matrix


m to this Matrix (note: this Matrix WILL BE CHANGED) ; it throws an exception if the matrix addition is not de ned (i.e, if the matrices do not have the same dimensions); the detail message of the exception should read: "Invalid operation".


5) public Matrix subMatrix(int i, int j) throws ArithmeticException – returns a new Matrix object, which represents a submatrix of this Matrix, formed out of rows 0 through i and columns 0 through j. The method should rst check if values i and j are within the required range, and throw an exception if any of them is not. The exception detail message should read: "Submatrix not de ned". Note: The new object should be constructed in such a way that changes in the new matrix do not a ect this Matrix.


6) public boolean isUpperTr() – returns true if this Matrix is upper trian-gular, and false otherwise. A matrix is said to be upper triangular if all elements below the main diagonal are 0. Note that the main diagonal contains the elements situated at positions where the row index equals the column in-dex. In the following ples the main diagonal contains elements 1,9,3.


ple of a 3-by-3 upper triangular matrix: 1 4 1 0 9 0 0 0 3



ple of a 3-by-4 upper triangular matrix:

1

5

1

4

0

9

6

6

0

0

3

8


ple of a 4-by-3 upper triangular matrix:


1 4 2


0 9 6


0 0 3


0 0 0


7) public static Matrix sum(Matrix[] matArray) throws ArithmeticException-returns a new matrix representing the sum of all matrices in matArray. The method throws an exception if the matrices do not have the same dimensions.


This method MUST USE method addTo() to perform the addition of two matrices.


8) public String toString() – returns a string representing the matrix, with each row on a separate line, and the elements in a row being separated by 2 blank spaces.

An n-by-n matrix a is said to be upper triangular if all elements below the main diagonal are 0. Such a matrix can be represented e  ciently by using only a one

dimensional array of size n(n+1)/2, which stores the matrix elements row by row, skipping the zeros below the diagonal, i.e., in the following order: a(0,0), a(0,1), a(0,2), , a(0,n-1), a(1,1), a(1,2), , a(1,n-1), a(2,2), a(2,3), , a(2,n-1) a(n-1,n-1). The Java class UpperTriangularMatrix has to model square upper triangular matrices of integers, stored in e cient format as described above. Class UpperTriangularMatrix should have two private instance variables: an integer to represent the matrix size (i.e. the number of rows n), and a one dimensional array to store the matrix elements in e cient format.


Class UpperTriangularMatrix contains at least the following constructors:


– public UpperTriangularMatrix(int n) – if n 0, changes n to 1; initializes the UpperTriangularMatrix object to represent the all-zero n-by-n matrix.


– public UpperTriangularMatrix(Matrix upTriM) throws IllegalArgumentException


– initializes the UpperTriangularMatrix object to represent the upper trian-gular matrix upTriM. Note that upTriM is an object of the class Matrix that you have to write for this project. The method throws an exception if upTriM is not upper triangular. To check if the upper triangular condition is satis ed you MUST USE the method isUpperTr() of class Matrix.


Class UpperTriangularMatrix contains at least the following instance methods:


– public int getDim() – returns the number of rows of this matrix.


– public int getElement(int i, int j) throws IndexOutOfBoundsException – returns the matrix element on row i and column j if i and j are valid indices


of this matrix (indexing starts at 0); otherwise an IndexOutOfBoundsException is thrown, with message "Invalid index".


– public void setElement(int x, int i, int j) throws IndexOutOfBoundsException, IllegalArgumentException – if i and j are valid indexes of the matrix, then


the element on row i and column j of the matrix is assigned the value x; however, if indexes i and j correspond to a position in the lower part of the matrix and x is not 0 then an IllegalArgumentException has to be thrown with message "Incorrect argument"; nally, if indexes i and j do not represent a valid position in the matrix then an IndexOutOfBoundsException is thrown, with message "Invalid indexes".


– public Matrix fullMatrix() – returns a Matrix object corresponding to this UpperTriangularMatrix. Note that the Matrix object will store the full matrix including all the zeros from the lower part.


– public void print1DArray() – prints the elements of the one dimensional array that stores the elements of the upper triangular part, separated by two spaces.


– public String toString() – returns a string representing this UpperTriangularMatrix object. The representation should show all elements of the full matrix with


each row on a separate line.


– public int getDet() – returns the determinant of the matrix, which equals the product of the elements on the main diagonal.


– public double[] effSolve(double[] b) throws IllegalArgumentException


– This method solves the matrix equation Ax=b, where A is this UpperTriangularMatrix,

if the determinant of A is non-zero. Otherwise it throws an exception. The method returns array x. The method has to be e cient, which means that it has to use an e cient way to solve the equation and implement it without wasting time or memory resources, in other words, without allocating arrays (except for x) or invoking other methods. Partial marks will be awarded for correct, but less e cient solutions. Note that the method should also check if the dimension of b is appropriate and if not throw an exception.


INSTRUCTIONS: You may implement public methods in class Matrix to return the number of rows and the number of columns.